Thin film condensation is commonly present in numerous natural and artificial processes. Phase-change driven passive heat spreaders such as heat pipes, which are widely used in electronics cooling, employ a continuous condensation process at the condenser region. When the wick structure of a heat pipe is composed of grooves, the top surfaces of the walls (fins) located between consecutive grooves function as the major source of condensation and the condensate flows along the fin top into the grooves. Modeling of this condensation problem is vital for the proper estimation of condensation heat transfer, which constitutes the basis for the overall performance of a heat pipe together with the evaporation process. In the current study, a solution methodology is developed to model the condensation and associated liquid flow in a fin-groove system. Conservation of mass and momentum equations, augmented Young-Laplace equation and Kucherov-Rikenglaz equation are solved simultaneously to calculate the film thickness profile. The model proposed enables the investigation of the effect of disjoining pressure on the film profile by keeping the fin-groove corner, where the film becomes thinnest, inside the solution domain. The results show that dispersion forces become effective for near isothermal systems with sharp fin-groove corners and the film profile experiences an abrupt change, a slope break, in the close proximity of the corner. The current study is the first computational confirmation of this behavior in the literature.